From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Wed, 27 Sep 2017 15:06:31 +0100 Subject: First commit on github -- NetBunch 1.0 --- doc/power_law.1.html | 217 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 217 insertions(+) create mode 100644 doc/power_law.1.html (limited to 'doc/power_law.1.html') diff --git a/doc/power_law.1.html b/doc/power_law.1.html new file mode 100644 index 0000000..7ebae1c --- /dev/null +++ b/doc/power_law.1.html @@ -0,0 +1,217 @@ + + + + + + power_law(1) - Sample N integers from a discrete power-law distribution + + + + + +
+ + + +
    +
  1. power_law(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. power_law(1)
    4. +
+ +

NAME

+

+ power_law - Sample N integers from a discrete power-law distribution +

+ +

SYNOPSIS

+ +

power_law gamma k_min k_max N

+ +

DESCRIPTION

+ +

power_law samples N elements from the discrete power-law +distribution

+ +
P(k) ~ k^{gamma}
+
+ +

where

+ +
k_min <= k <= k_max, gamma < 1
+
+ +

The program can be used to generate a power-law degree distribution +with an assigned value of the exponent <gamma.

+ +

PARAMETERS

+ + + + +

OUTPUT

+ +

power_law prints on the standard output the sampled values, one per +line, in the format:

+ +
s1
+s2
+s3
+ ...
+sN
+
+ +

The program returns the value 0 if the sum of the samples is even, +or returns 1 otherwise. The return value can be used to determine +whether the set of samples can correspond to a degree sequence (if the +sum of the sequence is odd, then the sequence cannot be a valid degree +sequence). See RETURN VALUES below.

+ +

EXAMPLES

+ +

To generate N=1000 independent samples from the power-law +distribution P(k) ~ k^(-3), where samples are in the interval +[3, 50], we can use:

+ +
$ power_law -3.0 3 50 1000
+11
+3
+3
+5
+6
+7
+ ....
+8
+3
+$
+
+ +

To save the samples in the file pl_-3.0_3_50_1000, we redirect STDOUT:

+ +
$ power_law -3.0 3 50 1000 > pl_-3.0_3_50_1000
+
+ +

RETURN VALUES

+ +

The value returned by power_law can be used to test whether the sum +of the resulting set of samples is even or odd. Under Windows +PowerShell, you can check the last exit code by inspecting the +variable $lastExitCode right after executing power_law, as in:

+ +
> power_law -2.7 4 300 5000 > pl_-2.7_4_300_5000
+> $lastExitCode
+
+0
+>
+
+ +

In this case, the exit code is 0, meaning that the resulting set of +samples has an even sum (and can be thus used as a degree +sequence). Under Linux/MacOS/Unix (and in general when using any +POSIX-compliant shell) you should check the value of the variable +$?, right after executing power_law, i.e.:

+ +
$ power_law -2.5 3 500 5000 > pl_-2.5_3_500_5000
+$ echo $?
+1
+$
+
+ +

Notice that this particular run of power_law has produced a sequence +with an odd sum, which thus cannot correspond to a valid degree sequence.

+ +

SEE ALSO

+ +

deg_seq(1), conf_model_deg(1), conf_model_deg_nocheck(1)

+ +

REFERENCES

+ + + + +

AUTHORS

+ +

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

+ + +
    +
  1. www.complex-networks.net
    2. +
  2. September 2017
    3. +
  3. power_law(1)
    4. +
+ +
+ + -- cgit v1.2.3